The 72 year old was one of Mr Trump's most vocal and high-profile supporters on the campaign trail.
He was New York's mayor during the September 11, 2001, attacks and led the city during the crisis following the destruction of the World Trade Center twin towers.
John Bolton, who served as U-S ambassador to the United Nations under President George W. Bush, is also reportedly under consideration for the high-profile job.
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特朗普任命的幕僚长亲台湾?